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AllQuestion and Answers: Page 318

Question Number 188207    Answers: 0   Comments: 0

Question Number 188203    Answers: 1   Comments: 0

Question Number 188196    Answers: 3   Comments: 2

(1)solve Diopthantine equation 754x+221y=13 (2) find the number abcd such that 4×(abcd)=dcba

$$\left(\mathrm{1}\right)\mathrm{solve}\:\mathrm{Diopthantine}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\mathrm{754x}+\mathrm{221y}=\mathrm{13} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{abcd}\: \\ $$$$\:\:\:\mathrm{such}\:\mathrm{that}\:\mathrm{4}×\left(\mathrm{abcd}\right)=\mathrm{dcba} \\ $$

Question Number 188195    Answers: 0   Comments: 0

Question Number 188192    Answers: 2   Comments: 0

prove that ∫_0 ^∞ e^(−a^2 x^2 ) cos(2bx) dx = ((√π)/(2a))e^(−b^2 /a^2 )

$$\:\:\: \\ $$$$\:\:\:\:{prove}\:{that} \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} {e}^{−{a}^{\mathrm{2}} {x}^{\mathrm{2}} } \mathrm{cos}\left(\mathrm{2}{bx}\right)\:{dx}\:\:\:=\:\:\:\frac{\sqrt{\pi}}{\mathrm{2}{a}}{e}^{−{b}^{\mathrm{2}} /{a}^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$

Question Number 188181    Answers: 0   Comments: 0

Question Number 188177    Answers: 2   Comments: 2

Question Number 188170    Answers: 1   Comments: 0

solve ⌊ cos (x )⌋ + ⌊ cos(x) +(1/2) ⌋+ ⌊ −2cosx ⌋ =0

$$ \\ $$$$\:\:\:\:\:\:{solve} \\ $$$$ \\ $$$$\:\lfloor\:{cos}\:\left({x}\:\right)\rfloor\:+\:\lfloor\:{cos}\left({x}\right)\:+\frac{\mathrm{1}}{\mathrm{2}}\:\rfloor+\:\lfloor\:−\mathrm{2}{cosx}\:\rfloor\:=\mathrm{0} \\ $$$$ \\ $$

Question Number 188164    Answers: 1   Comments: 1

Question Number 188163    Answers: 1   Comments: 2

Question Number 188158    Answers: 0   Comments: 0

Question Number 188156    Answers: 1   Comments: 0

a,b,c∈N 5a = 6b = 9c (abc)_(min) = ?

$$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N} \\ $$$$\mathrm{5a}\:=\:\mathrm{6b}\:=\:\mathrm{9c} \\ $$$$\left(\mathrm{abc}\right)_{\boldsymbol{\mathrm{min}}} \:=\:? \\ $$

Question Number 188155    Answers: 2   Comments: 0

Question Number 188147    Answers: 3   Comments: 0

Question Number 188151    Answers: 1   Comments: 0

Simplify: (√(1+(1/1^2 )+(1/2^2 ))) +(√(1+(1/2^2 )+(1/3^2 ))) +...+(√(1+(1/(2022^2 ))+(1/(2023^2 ))))

$$\mathrm{Simplify}: \\ $$$$\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }}\:+\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }}\:+...+\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2022}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2023}^{\mathrm{2}} }} \\ $$

Question Number 188128    Answers: 1   Comments: 0

Question Number 188126    Answers: 0   Comments: 0

In convex polygon ABCD AB = 10 (√6) , CD = 18 ∠ ABD = 60° , ∠ BDC = 45° and BD = 13 (√6) + 9 (√2) find AC = ?

$$\mathrm{In}\:\mathrm{convex}\:\mathrm{polygon}\:\:\mathrm{ABCD} \\ $$$$\mathrm{AB}\:=\:\mathrm{10}\:\sqrt{\mathrm{6}}\:\:,\:\:\mathrm{CD}\:=\:\mathrm{18} \\ $$$$\angle\:\mathrm{ABD}\:=\:\mathrm{60}°\:\:,\:\:\angle\:\mathrm{BDC}\:=\:\mathrm{45}° \\ $$$$\mathrm{and}\:\:\mathrm{BD}\:=\:\mathrm{13}\:\sqrt{\mathrm{6}}\:+\:\mathrm{9}\:\sqrt{\mathrm{2}} \\ $$$$\mathrm{find}\:\:\mathrm{AC}\:=\:? \\ $$

Question Number 188119    Answers: 1   Comments: 1

Question Number 188107    Answers: 2   Comments: 0

Question Number 188100    Answers: 2   Comments: 0

Question Number 188098    Answers: 1   Comments: 0

∫x!dx

$$\int\boldsymbol{\mathrm{x}}!\boldsymbol{\mathrm{dx}} \\ $$

Question Number 188095    Answers: 2   Comments: 4

Question Number 188094    Answers: 0   Comments: 1

Question Number 188092    Answers: 0   Comments: 0

Question Number 188086    Answers: 1   Comments: 0

I = ∫_0 ^∞ ((tan^(−1) (x/a))/(x(x^2 +b^2 )))dx

$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{I}\:\:\:=\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{tan}^{−\mathrm{1}} \left({x}/{a}\right)}{{x}\left({x}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)}{dx} \\ $$

Question Number 188083    Answers: 1   Comments: 3

determine the value of b for which y=((−x)/3) +b meets the graph of y^2 =x^3 orthogonally

$${determine}\:{the}\:{value}\:{of}\:{b}\:{for}\:{which}\: \\ $$$$\:\:\:{y}=\frac{−{x}}{\mathrm{3}}\:+{b}\:\:{meets}\:{the}\:{graph}\:{of} \\ $$$$\:{y}^{\mathrm{2}} ={x}^{\mathrm{3}} \:\:{orthogonally} \\ $$

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